I am currently using two monitors with one in landscape mode and the other in portrait mode. Video card is Nvidia Geforce 9600 GT with nvidia's propriety driver.

I was able to force the issue in 11.10 by assigning a separate X screen for each monitor and rotating the screen assigned to the portrait monitor. ( :0 for the landscape and :1 for the portrait)

I heard that 12.04 improved greatly on multi-monitor configurations. But it doesn't work for me: I had to resort to TwinView mode in order to take advantage of seamless multi-monitor experience but TwinView mode doesn't work with my situation where one of the monitor is in portrait mode!

Even worse, when I go back to my original configuration, i.e. separate X screens instead of TwinView, my portrait monitor shows only white screen with default X cursor without any of unity goodness.

I generated it using nvidia settings, not with twin view but with seperated X screens, screen 1 is absolute and screen 2 is Right Of. I checked Xinerama enabled.
Then I edited the xorg.conf file so that to add option for rotation of both screens (look at the file).
It worked!

I have a similar problem:
I have been using until today ubuntu 10.4, I did not bother upgrading it since it worked and I need a working station in my office. It work under strange configuration: I used xinerama in the xorg.conf file (find it in /etc/X11/) and rotated the screens with the options given by the nvidia driver

Option "Rotate" "left"

It worked, I wrote it long time ago. Now, I wanted to try ubuntu 3D or Gnome 3D, but it dones not work, maybe because xinerama does not work with thi nvidia driver and the 12.04 release. It DOES work with ubuntu 12.04 if you choose 'gnome classic', but not otherwise.
I tried to tweek with nvidia-settings program, but did not find any option to rotate the screens there.

Forgen xinerama! choose Twin View. Choose the left screen to be primary (absolute). the other one ABOVE the primary. then save the xorg file. edit it

sudo nano \etc\X11\xorg.conf

and add the rotation option to the screen Section. (Rotate left in my case).
Then I got a perfect dual screen with two monitors, rotated, beside each other..... :-)
Works only in unity, but not 3D. compiz is broken for now.
N

I vote to post about Nouveau open source driver. I had the problem with 2 monitors in Ubuntu 12.04 LTS with NVidia proprietary driver. The answer really helped. I installed synaptic, launched synaptic, found all that concerned nouveau and added those packages. After that two monitors started to work properly. And I managed them from Display settings in System parameters.